1. Field of the Invention
This invention relates to the field of control system design, and more specifically, to model error bounds computation for system identification.
2. Background Information
Robust control system design entails designing a uncertainty-tolerant system such that the stability of the system is maintained for all perturbations which satisfy the uncertainty bounds. Uncertainty may take any forms such as noise or disturbance signals and transfer function modeling errors. Uncertainty must be quantified and its bounds must be found, in order to determine if the system will remain stable or to determine the worst-case behavior given the uncertainty. As such, it is desirable to know how large can the uncertainty be before instability occurs or before performance degrades beyond a bound. Various robust control designs have been developed such as H.sub..infin. and .mu.-synthesis designs. H.sub..infin. robust control design enables stability performance and robustness properties of a system to be predicted with some certainty and it is developed to allow for modeling errors in system identification. The .mu.-synthesis design method uses repeated iterations of an H.sub..infin. design algorithm and invokes the structured singular value of the transfer function matrix of a system to test whether the design is robust.
Currently available software design methods for determining the model error bounds for system identification of stochastic models are however unsuitable (or incompatible) for use with robust control design methods. One major drawback of the identification methods that account for stochastic processes is that they provide model error bounds that are in terms of covariance of estimated parameters of the model structure or covariance of estimated transfer functions. However, because robust control design requires model error bounds to take the specific form known as "additive or multiplicative frequency-weighted singular value bounds", the model error bounds in terms of covariance cannot be used directly in robust control design methods. There are several software design tools developed for robust control and system identification such as: Matlab.RTM. Control Module and System Identification Module, Matlab.RTM. .mu.-synthesis Toolbox, Matlab.RTM. System Identification Toolbox (all available from Mathworks, Inc., Natick, Mass.), and MATRIXx.RTM. Robust Control Module and System Identification Module (available from Integrated Systems, Inc., Sunnyvale, Calif.). However, these current design tools do not allow computer automated or computer guided method to generate the model uncertainty from system identification in a mathematically compatible format usable in robust control design.
Moreover, for multi-input multi-output (MIMO) systems, the current design tools compute the self and cross variance of every pair of transfer function from the covariance of estimated parameters. These computations are impractical not only because the resulting pair-wise covariance cannot be directly used in robust control design, but also because these computations cannot be handled by ordinary workstations. Therefore, the available computing methods are laborious, time-consuming, and very expensive.
Additionally, when model order selection methods such as Akaike's Criterion, Modified Akaike's Criterion, or Rissanen's Minimum Descriptor Length Criteria are used with input-output data from closed-loop tests, biases in parameter estimates are unavoidable. These biases make model error bounds from covariance of estimated parameters incorrect. Thus, what is needed is a method for computing model error bounds for stochastic systems such that they are directly useable in H.sub..infin. and .mu.-synthesis robust control design methods.